Question Bank • QB_SWCE_SM_007 NAT • 2 Marks

Section 4: Soil and Water Conservation Engineering

Soil Mechanics

Subtopic: Terzaghi's one dimensional soil consolidation theory

Question Statement:

A clay layer of thickness $4.0\text{ m}$ is bounded by permeable sand layers at both top and bottom (double drainage). The coefficient of consolidation is $C_v = 2.0 \times 10^{-7}\text{ m}^2\text{/s}$. The time factor for $50\%$ consolidation is $T_v = 0.197$. The time required to reach $50\%$ consolidation in days is ________ (round off to 1 decimal place).

Answer Key:

45.6

Step-by-Step Solution & Explanation

1. For double drainage, maximum drainage path $d = H/2 = 4.0 / 2 = 2.0\text{ m}$. 2. Time for consolidation: $t = \frac{T_v \cdot d^2}{C_v} = \frac{0.197 \times (2.0)^2}{2.0 \times 10^{-7}} = \frac{0.197 \times 4.0}{2.0 \times 10^{-7}} = \frac{0.788}{2.0 \times 10^{-7}} = 3.94 \times 10^6\text{ s}$ 3. Converting to days: $t = \frac{3.94 \times 10^6}{86400} \approx 45.60\text{ days} \approx 45.6\text{ days}$
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